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Parikh vectors
1SRL_1 9CHV_1 9DRF_1 Letter Amino acid
3 28 9 D Aspartic acid
7 26 16 G Glycine
2 40 14 I Isoleucine
2 27 6 K Lycine
5 26 19 A Alanine
2 18 7 Q Glutamine
0 14 5 M Methionine
8 20 10 T Threonine
2 17 16 R Arginine
4 22 25 E Glutamic acid
1 6 12 H Histidine
6 43 20 L Leucine
2 8 4 W Tryptophan
3 19 6 N Asparagine
2 33 7 F Phenylalanine
2 9 6 P Proline
5 22 13 S Serine
4 15 6 Y Tyrosine
4 44 17 V Valine
0 12 0 C Cysteine 

1SRL_1|Chain A|SRC TYROSINE KINASE SH3 DOMAIN|Gallus gallus (9031)
>9CHV_1|Chain A|Beta-2 adrenergic receptor,Calcineurin subunit B type 1|Homo sapiens (9606)
>9DRF_1|Chains A, B, C, D, E, F, G, H|ADP-ribose pyrophosphatase|Klebsiella pneumoniae (573)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
1SRL , Knot 36 64 0.78 36 56 62 
GALAGGVTTFVALYDYESRTETDLSFKKGERLQIVNNTEGDWWLAHSLTTGQTGYIPSNYVAPS
9CHV , Knot 184 449 0.83 40 237 423 
DEVWVVGMGIVMSLIVLAIVFGNVLVITAIAKFERLQTVTNYFITSLACADLVMGLAVVPFGAAHILMKMWTFGNFWCEFWTSIDVLCVTASIETLCVIAVDRYFAITSPFKYQSLLTKNKARVIILMVWIVSGLTSFLPIQMHWYRATHQEAINCYAEETCCDFFTNQAYAIASSIVSFYVPLVIMVFVYSRVFQEAKRQLDADEIKRLGKRFKKLDLDNSGSLSVEEFMSLPELQQNPLVQRVIDIFDTDGNGEVDFKEFIEGVSQFSVKGDKEQKLRFAFRIYDMDKDGYISNGELFQVLKMMVGNNLKDTQLQQIVDKTIINADKDGDGRISFEEFCAVVGGLDIHKKMVVDVKFCLKEHKALKTLGIIMGTFTLCWLPFFIVNIVHVIQDNLIRKEVYILLNWIGYVNSGFNPLIYCRSPDFRIAFQELLCLRRDDLKAYGNGY
9DRF , Knot 98 218 0.80 38 148 210 
MAHHHHHHMSKPTQQGITFSKNDVEIIARETLYRGFFSLDLYRFRHRLFNGGMSGEITREIFERGHAAVLLPFDPVRDEVVLVEQIRIAAYDTSESPWLLEMVAGMIEAGETVEDVARREALEEAGLEVGRTKPILSYLASPGGTSERLSILVGEVDASTAKGIHGLAEENEDIRVHVVSREQAYQWVEEGKIDNAASVIALQWLQLHYHNLRNEWTK

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(1SRL_1)}(2) \setminus P_{f(9CHV_1)}(2)|=18\), \(|P_{f(9CHV_1)}(2) \setminus P_{f(1SRL_1)}(2)|=199\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:1111111001111000000000010100100101100001011110010010010110001110
Pair \(Z_2\) Length of longest common subsequence
1SRL_1,9CHV_1 217 4
1SRL_1,9DRF_1 156 3
9CHV_1,9DRF_1 177 4

Newick tree

 
[
	9CHV_1:10.07,
	[
		1SRL_1:78,9DRF_1:78
	]:27.07
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{513 }{\log_{20} 513}-\frac{64}{\log_{20}64})=136.\)
Status Protein1 Protein2 d d1/2
Query variables 1SRL_1 9CHV_1 171 97.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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